论文标题
循环量子宇宙学中的正规化和量子动力学
Regularizations and quantum dynamics in loop quantum cosmology
论文作者
论文摘要
环路量子重力（LQG）和宇宙学（LQC）的关键组成部分之一 - Thiemann正则化程序是非唯一的。特定处方的不同选择会导致模型在数学结构和物理预测上都不同。在这里，我们简要回顾了文献中在各向同性LQC中提出的一组此类处方，例如具有无质量标量物质含量的平坦宇宙。对于到目前为止所研究的至少研究的，进一步称为Yang-ding-ma处方，对其数学结构和结果量子动力学进行了详细分析，确认并扩展了通过现象学方法获得的结果。为了探测动力学，设计了一种相对健壮的方法（在宏观宇宙的近似中起作用）评估量子轨迹。所述方法是半经典处理的一种变体，它允许通过内部时钟的函数和一组某些中心矩进行分析表达轨迹 - 运动的常数以系统的方式编码量子校正到任意顺序。作为对方法对量子轨迹的鲁棒性类似评估的测试，该量子轨迹是针对其他处方的量子轨迹进行的。进一步简要讨论了治疗的局限性。
One of critical components of Loop Quantum Gravity (LQG) and Cosmology (LQC) -- Thiemann regularization procedure is non-unique. Different choices of particular prescriptions lead to models which differ in both mathematical structure and physical predictions. Here we briefly recall a set of such prescriptions proposed in the literature in context of isotropic LQC on the example of a flat universe with massless scalar matter content. For the one least investigated so far, further called Yang-Ding-Ma prescription, a detailed analysis of its mathematical structure and resulting quantum dynamics is performed, confirming and extending the results obtained so far by phenomenological methods. In order to probe the dynamics, a relatively robust method (working in the approximation of the macroscopic universe) of evaluating quantum trajectories is devised. Said method is a variant of a semiclassical treatment that allows to express the trajectories analytically as function of internal clock and a set of certain central moments -- constants of motion encoding quantum corrections up to arbitrary order in systematic manner. As a test of method's robustness analogous evaluation of the quantum trajectory in volume is performed for those of other prescriptions, for which it is applicable. The limitations of the treatment are further briefly discussed.
